(a) You are provided a retort stand, a spring balance, masses, a beaker containing water, another beaker containing a liquid labelled, L, and other necessary apparatus.

(i) Suspend the mass, m = 20 g on the spring balance and measure the weight in air, W\(_A\) in Newton.

(ii) Immerse the suspended mass completely in water and measure weight in water, W\(_W\) in Newton. Evaluate U\(_1\) = W\(_A\) - W\(_W\).

(iii) Immerse the suspended mass completely in the liquid L of the same volume with water and measure the weight in liquid W\(_L\). Evaluate U\(_2\) = W\(_A\) - W\(_L\).

(iv) Repeat the procedure for m = 40g, 60g, 80g, and 100g respectively. In each case, evaluate \(W_A\), W\(_W\), U\(_1\), W\(_L\), U\(_2\).

(v) Tabulate the readings.

(vi) Plot a graph of U\(_1\) on the vertical axis and U\(_2\) on the horizontal axis starting both axes from the origin (0, 0).

(vii) Determine the slope s of the graph

(viii) Evaluate K = \(\frac{1}{\text{s}}\)

(ix) State two precautions taken to ensure accurate results.

b(i) State the Archimedes' principle,

(ii) State two differences between density and relative density